Natural gas as a clean, low-carbon energy will play an important role in the world's low-carbon energy transformation. In this paper, research on the elasticity of natural gas demand is surveyed, and it is found that the price and income elasticities of natural gas demand in different sectors are distinctive. In particular, this paper constructs an autoregressive distribution lag model to study the elasticity of natural gas demand in various sectors of China. The results show that, except for the residents sector, the long-run price elasticity of natural gas demand in other sectors is greater than 0, which is contrary to the estimates of developed countries. The demand for natural gas is complementary to coal in industrial and power generation sectors, which is also different from developed countries. The elasticity of natural gas demand in residents sector is lack in price elasticity but abundant in income elasticity, which is similar to the developed countries. The results also shows that natural gas and oil are substitutes for each other in the transportation sector, and natural gas and coal are substitutes for each other in service sector.